I would guess it is more profile and how much wood you both expect to remove and how much surface area you have in contact with the wood.
The shank size is only the first indication. I haven't seen any 1/4" bits that 'Need' to be mounted in a router table. However that doesn't mean that you can't benefit from doing so.
The larger shank bits allow for a larger torque to be placed on them and to be used in larger machines. They also will tend to have less vibration movement for a cleaner cut (At least that is what I have read).
When it is easy to use my Shaper (like a mounted table router but slower and more powerful) I will. Bits that cut the 'tongue' in tongue and groove, raised panel bits, shapers for moldings and such should really be mounted in a table for best results and safest practices.
But just because it's a 1/2" shank doesn't mean you have to use it that way. If it is a 3/4" straight bit on a 1/2" shank it will be just as safe as a 1/4" shank, and will likely have a cleaner cut. I would like to replace all my bits with 1/2" shank bits (at least the ones that I can)